Chapter 7, Problem 6CRE

a.

To determine

To find: The probability that WAIS score of selected individuals is 105 or above.

Answer to Problem 6CRE

The probability is 0.3707.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population mean }\left(\mu \right)=100\\ \text{Population standard deviation}\left(\sigma \right)=15\\ \text{Sample size}\left(n\right)=60\end{array}$

The probability that WAIS score of selected individuals is 105 or abovecan be calculated as:

  $\begin{array}{c}P\left(x>29\right)=P\left(Z>\frac{105-100}{15}\right)\\ =P\left(Z>0.33\right)\\ =0.3707\end{array}$

Thus, the probability is 0.3707.

b.

To determine

To find: The mean and standard deviation of the sampling distribution

Answer to Problem 6CRE

The required mean and standard deviation are 100 and 1.937 respectively.

Explanation of Solution

The mean and standard deviation can be calculated as:

  $\begin{array}{c}{\mu }_{\overline{x}}=\mu =100\\ {\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}\\ =\frac{15}{\sqrt{60}}\\ =1.937\end{array}$

The required mean and standard deviation are 100 and 1.937 respectively.

c.

To determine

To find: The probability that average WAIS score is above 105 or more.

Answer to Problem 6CRE

The probability is 0.0049.

Explanation of Solution

The probability that average WAIS score is above 105 or morecan be calculated as:

  $\begin{array}{c}P\left(\overline{x}>105\right)=P\left(Z>\frac{105-100}{\frac{15}{\sqrt{60}}}\right)\\ =P\left(Z>2.58\right)\\ =0.0049\end{array}$

Thus, the probability is 0.0049.

d.

To determine

To explain: Whether the answer of above parts will be affected if the distribution of WAIS score is said non normal.

Explanation of Solution

The answer of (a) would be affected if the distribution is said non-normal.

On the other hand, the answers of b and c would not be affected because the sample size is above 30.